Formatio of A Supergai Array ad ts Applicatio i Radar Tra Cao Quye, Do Trug Kie ad Bach Gia Duog. Research Ceter for Electroic ad Telecommuicatios, College of Techology (Coltech, Vietam atioal Uiversity, Haoi (VUH. Faculty of Physics, Haoi Uiversity of Scieces, Vietam atioal Uiversity, Haoi (VUH Abstract- The formatio of a liear array is itroduced i []. Whe all of the elemet fields are i phase, we obtaied a mai beam with its maximum directivity. The pheomeo i which a liear array be able to have a gai which is higher tha the maximum directivity of the ormal liear array called superdirectivity [,3,4]. this paper, we study the formatio of a supergai array ad its applicatio i Radar, some simulatios are give to illustrate the array performace ad some remark coclusios are give.. TRODUCTO Radar moder, we iterested i desig a system havig a very arrow beam ad very high directivity. geeral, i order to do so we have use a large array which is icoveiet i electroic-battle ow a day. Therefore, the researches about super gai array have much attractive from Radar was bor up to ow. this paper, the formatio of a supergai array ad its applicatios i Radar are preseted. The paper is orgaized as follows. The directivity of a liear array is itroduced i part. Part presets supergai array. Part V presets simulatio results. Part V discusses the applicatio of the supergai array i Radar. The coclusios are give i part V.. DRECTVTY OF A LEAR ARRAY Cosider the case of a uiformly spaced liear array laid out alog the z axis. We assume that the currets have equal amplitudes but a uiform progressive phase, i.e. = exp( j ( With is a costat called the phase-shift factor. Uder this assumptio, the array factor is give by [ j( kd cosθ ] A ( θ = exp ( f the elemet patter is isotropic, the directivity is govered etirely by the array factor. t is defied as the power i the directio of the mai beam maximum divided by the average power desity from the array. Thus
* = A( θ A ( θ D (3 * A( θ A ( θ r siθdθdφ 4r Where r is the distace from the atea to the observatio poit, θ is the agle from the boresight to the observatio poit, θ is the agle from the boresigt to the mai beam maximum. akig use of ( ad d equals λ /, this becomes D ( = which is a most iterestig formula i several respects. The directivity as give by (4, tur out to be a measure of the coheret of radiatio from the liear array. The umerator is proportioal to the total coheret field, squared, whereas the deomiator is proportioal to the sums of the squares of the idividual fields from each elemet. Furthermore, the directivity as give by (4 is see to be idepedet of sca agle. O the face of it, this seems surprisig, sice we have already observed that the mai beam broades as it is scaed away from broadside, a maifestatio which usually sigifies lowered directivity. However, for a liear array, as the coical beam is scaed toward edfire, the core teds to occupy a smaller solid agle i space, a effect which just cacels the beam broadeig. This compesatio holds util the beam approaches edfire, whe aother compesatio takes over- the appearace of a secod mai beam at reverse edfire. Whereas, (4 is idepedet of sca agle, it is ot idepedet of curret distributio. The excitatio ca be expressed usig the Fourier series descriptio P = a exp( jp p p= P + Where P is the highest spatial harmoic eeded to represet the distributio, pure real because the distributio is assumed to be symmetric. Therefore, oe fid that Thus, (4 becomes D = ( + a P = ( + a p P = P P + ( a p / a For half-wave spacig, L = ( + ( λ / ad uiform distributio, (7 becomes D = L / λ (8 (4 (5 (6 (7 a p = a is p
. SUPERGA ARRAY From (8, it is clearly that if we do ot make ay special chages i iter-elemet space or the phase excitatio, the maximum directivity of the ormal liear array beig limited by the umber of elemet used. Defie ψ as ψ = ( kd cosθ (9 Assumig a edfire array with d is equal to half wave legth, the phase shift factor is equal to kd, all elemet are isotropic radiatio. The array factor is give by si( ψ A ( θ = ( siψ Hase ad Woodward i [] proposed to sca the beam further tha edfire, this causes a icrease i the sidelobe level, but makes the visible portio of the mai beam have a steeper average slope, givig rise to a icreased directivity. The maximum directivity resulted whe approximately half the mai beam was scaed out of the visible regio. aother way, the phase progressive i the costrai is give by s ± ( kd + ( The directivity of the supergai array is approximately give by D s = 7.8L / λ ( V. SULATO RESULTS Usig atlab program, we obtaied the array factors of the edfire array with varyig from to 6 as show i Figure 4 to 6. To compariso purpose, we simulate the array factors of the supergai array with d =.3λ ad correspodigly as i show i Figure to 3. From the Figure 4 to 6, we ca see that the more elemet are used the arrower beam width obtaied. Whe comparig three couples of figure, i.e. (,4, (,5, (3,6, the mai beam width of the supergai array is always arrower tha the oe of the ormal edfire array. Figure to 3, it is clearly that the maximum of the mai beam of the supergai array is out of the visible regio. This caused a icreasig of trasmitted eergy i the mai beam compared to the average trasmitted eergy i visible regio. Therefore, there is a ehaced directivity.
V. APPLCATOS TO RADAR A Radar s atea system should have very high directivity, so we suggest to use two supergai arrays with two elemets ( Ds =.84 combiig with sigal processig. As i [4], i priciple, to obtai the super directioal patter we have to realize the directioal patter with the phase jump by i ay directio, while the amplitude i that directio remais the same. A typical phase characteristic eeded for such purpose is show i the Figure 7 as follows Φ ( Φ ( Figure 7. Phase patter of the first ad secod array Whe usig two arrays, the phase patters of which are axial-symmetrical to each other, we readily to see that withi the iterval of directio ± δ, with δ, we trasmit the maximum voltage, while i the other directio we trasmit othig. t is evidet because i directio δ + the trasmitted sigal from both array are quite i phase, but i the other directio the sigal are quite ati-phase to each other. Fially, the Radar s atea system has superdirectivity ot oly by supergai array but also by usig axial-symmetrical phase scheme. V. COCLUSOS A Radar s atea system is itroduced usig two supergai arrays with two elemets combiig with the axial-symmetrical phase scheme. ts high performace is very attractive but the realizatio of the system should be ivestigated. REFERECES [] R.C Hase, icrowave Scaig Ateas, Volume, Academic Press, 966. [] W.W.Hase ad J.R.Woodyard, A ew Priciple i Directioal Atea Desig, Proceedig of RE, Volume 6, o 3, arch, 938. [3] Arthur D.Yaghjia el al, Electrical Small Supergai Edfire Arrays, Radio Sciece, Vol 43, arch,8. [4] Pha Ah, Ateas Without Phase Ceters ad Their Applicatios i Radio Egieerig, oograph, Wroclaw, 986. SS: 34-938.